Abstract:
When designing curves on surfaces the need arises to approximate a given noisy target shape by a smooth fitting shape. We discuss the problem of fitting a Bspline curve to a point cloud by squared distance minimization in the case that both, the point cloud and the fitting curve, are constrained to lie on a smooth manifold. The onmanifold constraint is included by using the first fundamental form of the surface for squared distance computations between the point cloud and the fitting curve. For the solution we employ a constrained optimization algorithm that allows us to include further constraints such as onesided fitting or surface regions that have to be avoided by the fitting curve. We illustrate the effectiveness of our algorithm at hand of several examples showing different applications.
Bibtex:
@article{floery2007ccfm, author = "Simon Fl{\"o}ry and Michael Hofer", title = "Constrained curve fitting on manifolds", journal = "ComputerAided Design", volume = "40", number = "1", pages = "2534", year= "2008", }

